A note on the pyjama problem
This note concerns the so-called pyjama problem, whether it is possible to cover the plane by finitely many rotations of vertical strips of half-width ε. We first prove that there exist no periodic coverings for ε<1/3. Then we describe an explicit (non-periodic) construction for ε=1/3 - 1/48. Fin...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/106094 http://hdl.handle.net/10220/17933 http://dx.doi.org/10.1016/j.ejc.2013.03.001 |
| _version_ | 1826121262510899200 |
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| author | Malikiosis, R.D. Matolcsi, M. Ruzsa, I.Z. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Malikiosis, R.D. Matolcsi, M. Ruzsa, I.Z. |
| author_sort | Malikiosis, R.D. |
| collection | NTU |
| description | This note concerns the so-called pyjama problem, whether it is possible to cover the plane by finitely many rotations of vertical strips of half-width ε. We first prove that there exist no periodic coverings for ε<1/3. Then we describe an explicit (non-periodic) construction for ε=1/3 - 1/48. Finally, we use a compactness argument combined with some ideas from additive combinatorics to show that finite coverings exist for all ε>1/5. The question whether ε can be arbitrarily small remains open. |
| first_indexed | 2024-10-01T05:29:49Z |
| format | Journal Article |
| id | ntu-10356/106094 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:29:49Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/1060942019-12-06T22:04:27Z A note on the pyjama problem Malikiosis, R.D. Matolcsi, M. Ruzsa, I.Z. School of Physical and Mathematical Sciences DRNTU::Science::Physics This note concerns the so-called pyjama problem, whether it is possible to cover the plane by finitely many rotations of vertical strips of half-width ε. We first prove that there exist no periodic coverings for ε<1/3. Then we describe an explicit (non-periodic) construction for ε=1/3 - 1/48. Finally, we use a compactness argument combined with some ideas from additive combinatorics to show that finite coverings exist for all ε>1/5. The question whether ε can be arbitrarily small remains open. 2013-11-29T06:28:33Z 2019-12-06T22:04:27Z 2013-11-29T06:28:33Z 2019-12-06T22:04:27Z 2013 2013 Journal Article Malikiosis, R., Matolcsi, M., & Ruzsa, I. (2013). A note on the pyjama problem. European journal of combinatorics, 34(7), 1071-1077. 0195-6698 https://hdl.handle.net/10356/106094 http://hdl.handle.net/10220/17933 http://dx.doi.org/10.1016/j.ejc.2013.03.001 en European journal of combinatorics |
| spellingShingle | DRNTU::Science::Physics Malikiosis, R.D. Matolcsi, M. Ruzsa, I.Z. A note on the pyjama problem |
| title | A note on the pyjama problem |
| title_full | A note on the pyjama problem |
| title_fullStr | A note on the pyjama problem |
| title_full_unstemmed | A note on the pyjama problem |
| title_short | A note on the pyjama problem |
| title_sort | note on the pyjama problem |
| topic | DRNTU::Science::Physics |
| url | https://hdl.handle.net/10356/106094 http://hdl.handle.net/10220/17933 http://dx.doi.org/10.1016/j.ejc.2013.03.001 |
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